There are a great deal of books on introductory analysis in print today, many written by mathematicians of the first rank. The publication of another such book therefore warrants a defense. I have taught analysis for many years and have used a variety of texts during this time. These books were of excellent quality mathematically but did not satisfy the needs of the students I was teaching. They were written for mathematicians but not for those who were first aspiring to attain that status. The desire to fill this gap gave rise to the writing of this book. This book is intended to serve as a...

Research in the past thirty years on the foundations of thermodynamics has led not only to a better understanding of the early developments of the subject but also to formulations of the First and Second Laws that permit both a rigorous analysis of the consequences of these laws and a substantial broadening of the class of systems to which the laws can fruitfully be applied. Moreover, modem formulations of the laws of thermodynamics have now achieved logically parallel forms at a level accessible to under- graduate students in science and engineering who have completed the standard calculus...

This book is intended for students familiar with a beginner's version of differential and integral calculus stressing only manipulation offormulas and who are now looking for a closer study of basic concepts combined with a more creative use of information. The work is primarily aimed at students in mathematics, engineering, and science who find themselves in transition from elementary calculus to rigorous courses in analysis. In addition, this book may also be of interest to those preparing to teach a course in calculus. Instead of exposing the reader to an excess of premature abstractions...

The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How- ever, it is a...

In the second edition of this popular and successful text the number of exercises has been drastically increased (to a minimum of 25 per chapter); also a new chapter on the Jordan normal form has been added. These changes do not affect the character of the book as a compact but mathematically clean introduction to linear algebra with particular emphasis on topics that are used in the theory of differential equations.

Cryptography is a key technology in electronic security systems. Modern cryptograpic techniques have many uses, such as to digitally sign documents, for access control, to implement electronic money, and for copyright protection. Because of these important uses it is necessary that users be able to estimate the efficiency and security of cryptographic techniques. It is not sufficient for them to know only how the techniques work. This book is written for readers who want to learn about mod ern cryptographic algorithms and their mathematical foundation but who do not have the necessary...

This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises,...

The purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica- tions which accompany them. The very talented students, with an ob- vious aptitude for mathematics, will rapidly require a course in functions of one real variable, more or less as it is understood by professional is not primarily addressed to them (although mathematicians. This book I hope they will be able to acquire from it a good introduction at an early age). I have not written this course in the style I would use for an advanced monograph,...

The first course in Analysis, which follows calculus, along with other courses, such as differential equations and elementary linear algebra, in the curricu- lum, presents special pedagogical challenges. There is a change of stress from computational manipulation to "proof. " Indeed, the course can become more a course in Logic than one in Analysis. Many students, caught short by a weak command of the means of mathematical discourse and unsure of what is expected of them, what "the game" is, suffer bouts of a kind of mental paralysis. This text attempts to address these problems in several...

GEOMETRY: Plane and Fancy offers students a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well known parallel postulate of Euclid. The author shows how alternatives to Euclid's fifth postulate lead to interesting and different patterns and symmetries. In the process of examining geometric objects, the author incorporates the algebra of complex (and hypercomplex) numbers, some graph theory, and some topology. Nevertheless, the book has only mild prerequisites. Readers are assumed to...